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Kernel quantile estimators in the dose-effect dependence

  • International Seminar “Probabilistic Models and Statistical Inference”
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Abstract

Nonparametric quantile estimators in the dose-effect dependence are considered. It is shown that these estimators are consistent and asymptotically normal. Limiting variances of the constructed estimators are given.

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References

  1. Kibzun, A.I. and Matveev, E.L., Optimization of the quantile function on the basis of kernel estimates, Autom. Remote Contr., 2007, vol. 68, pp. 64–74.

    Article  MathSciNet  MATH  Google Scholar 

  2. Kan, Yu.S. and Kibzun, A.I., Zadachi stokhasticheskogo programmirovaniya s veroyatnostnymi kriteriyami (Problems of Stochastic Programming with Probability Criteria), Moscow: Fizmatlit, 2009.

    MATH  Google Scholar 

  3. Holton, G.A., Value-at-Risk. Theory and Pratice Academic, 2003.

    Google Scholar 

  4. Araujo, S.P., Excess, Durations and Forecasting Value-at-Risk Universidade de Lisboa, 2011.

    Google Scholar 

  5. Krishtopenko, S.V., Tikhov, M.S., and Popova, E.B., Doza-effekt (Dose-Effect), Moscow: Meditsina, 2008.

    Google Scholar 

  6. Smirnov, N.V., Limiting laws for terms of variation series, Trudy Matem. Inst., 1949, vol. 25, pp. 5–59.

    Google Scholar 

  7. Falk, M., Asymptotic normality of the kernel quantile estimator, Ann. Statist., 1985, vol. 13, pp. 428–433.

    Article  MathSciNet  MATH  Google Scholar 

  8. Sun, S., Central limit theorem of the perturbed sample quantile for a sequence of M-dependent nonstationary random process, Teor. Veroyat. Primen., 1995, vol. 40, pp. 143–158.

    MATH  Google Scholar 

  9. Lio, Y.L. and Padgett, W.J., Some convergence results for kernel-type quantile estimators under censoring, Statistics Probab. Lett., 1987, vol. 5, pp. 5–14.

    Article  MathSciNet  MATH  Google Scholar 

  10. Ghorai, J.K., Estimation of a smooth quantile function under the proportional hazards model, Ann. Inst. Statist. Math., 1991, vol. 43, pp. 747–760.

    Article  MathSciNet  MATH  Google Scholar 

  11. Natanson, I.P., Teoriya funktsii veshchestvennoi peremennoi (Theory of Real Variable Function), Moscow: Nauka, 1974.

    Google Scholar 

  12. Niederreiter, H., Random Number Generation and Quasi-Monte Carlo Methods Philadelphia: Society for Industrial and Applied Mathematics, 1992.

    Book  MATH  Google Scholar 

  13. Dette, H., Neumeyer, N., and Pilz, K.F., A note on nonparametric estimation of the effective dose in quantal bioassay, J. Am. Statist. Assoc., 2005, vol. 100, pp. 503–510.

    Article  MathSciNet  MATH  Google Scholar 

  14. Tikhov, M.S., Estimation of the effective dose in dose-effect dependence over random experiment plans, in Statisticheskie metody otsenivaniya i proverki gipotez: mezhvuz. sb. nauchn. tr. Perm. un-t (Statistical Methods of Hypothesis Estimation and Verification. Coll. Papers Perm. Univ.), Perm, 2012, pp. 84–99.

    Google Scholar 

  15. Tikhov, M. and Borodina, T., A Nonparametric estimator for effective doses in dose-effect dependence over random experiment plans, Proc. 12th Int. Conf. ‘Reliability and Statistics in Transportation and Communication’, Riga, 2012.

    Google Scholar 

  16. Hengatrner, N.W., Asymptotic unbiased density estimators, ESIAM, 2009, vol. 13, no. 4, pp. 1–14.

    Google Scholar 

  17. Gnedenko, B.V., Kurs teorii veroyatnostei (Probability Theory Course), Moscow: URSS, 2005.

    Google Scholar 

  18. Tikhov, M.S. and Krishtopenko, D.S., Estimation of distributions in dose-effect dependence at the fixed plan of experiment, in Statisticheskie metody otsenivaniya i proverki gipotez: mezhvuz. sb. nauchn. tr., Perm. un-t (Statistical Methods of Hypothesis Estimation and Verification. Coll. Papers Perm. Univ.), Perm, 2006, pp. 66–77.

    Google Scholar 

  19. Hardle, W., Applied Nonparametric Regression Bonn: Econometric Society Monographs, 1992.

    Google Scholar 

  20. Hardle, W., Muller, M., Sperlich, S., and Werwatz, A., Nonparametric and Semiparametric Models Berlin: Springer-Verlag, 2004.

    Book  Google Scholar 

  21. Li, Q. and Racine, J.S., Nonparametric Econometrics: Theory and Practice New York: Princeton University, 2007.

    MATH  Google Scholar 

  22. Racine, J.S., Nonparametric Econometric Method Emerald Group Publ., 2009.

    Google Scholar 

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Correspondence to M. S. Tikhov.

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Original Russian Text © M.S. Tikhov, T.S. Borodina, 2013, published in Avtomatika i Vychislitel’naya Tekhnika, 2013, No. 2, pp. 29–43.

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Tikhov, M.S., Borodina, T.S. Kernel quantile estimators in the dose-effect dependence. Aut. Control Comp. Sci. 47, 75–86 (2013). https://doi.org/10.3103/S0146411613020089

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  • DOI: https://doi.org/10.3103/S0146411613020089

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